Question

ABCD and BCFE are parallelograms. If area of triangle EBC = 480 cm²; AB = 30 cm and BC = 40 cm.

Calculate : 
(i) Area of parallelogram ABCD;
(ii) Area of the parallelogram BCFE;
(iii) Length of altitude from A on CD;
(iv) Area of triangle ECF.

Answer 1

(i) Since ΔEBC and parallelogram ABCD are on the same base BC and between the same parallels i.e. BC // AD.

∴ A( ΔEBC ) = `1/2` x A( parallelogram ABCD )

parallelogram ABCD = 2 x A( ΔEBC )
                                  = 2 x 480 cm²
                                  = 960 cm²
(ii) Parallelograms on same base and between same parallels are equal in area.
Area of BCFE = Area of ABCD = 960 cm²

(iii) Area of triangle ACD=480 = `1/2` x 30 x Altitude
Altitude = 32 cm

(iv) The area of a triangle is half that of a parallelogram on the same base and between the same parallels.
Therefore,
Area( ΔECF ) = `1/2` Area(`square`CBEF )
Similarly, Area( ΔBCE ) = `1/2`Area(`square`CBEF )

⇒ Area( ΔECF ) = Area( ΔBCE ) = 480 cm².